Propiedades de secciones: fórmulas de centroide y momento de inercia

Fórmulas de área, centroide y momento de inercia de 27 secciones, desde figuras básicas hasta perfiles de acero. El momento de inercia respecto a los ejes centroidales es el que necesitas para esfuerzos de flexión y deflexiones.

Abre cada sección para ver todas sus propiedades (inercia respecto a la base, módulo plástico, constante de torsión), o pulsa Calcular para obtener los valores con tus medidas.

Figuras básicas

Sección	Área	Centroide	Inercia respecto a x̄	Inercia respecto a ȳ
Cuadrado	$$A = l^2$$	$$\bar{x} = \frac{l}{2}$$ $$\bar{y} = \frac{l}{2}$$	$$\bar{I}_x = \frac{l^4}{12}$$	$$\bar{I}_y = \frac{l^4}{12}$$	Calcular →
Cuadrado girado (rombo)	$$A = l^2$$	$$\bar{x} = \frac{l}{\sqrt{2}}$$ $$\bar{y} = \frac{l}{\sqrt{2}}$$	$$\bar{I}_x = \frac{l^4}{12}$$	$$\bar{I}_y = \frac{l^4}{12}$$	Calcular →
Rectángulo	$$A = b h$$	$$\bar{x} = \frac{b}{2}$$ $$\bar{y} = \frac{h}{2}$$	$$\bar{I}_x = \frac{b h^3}{12}$$	$$\bar{I}_y = \frac{b^3 h}{12}$$	Calcular →
Rectángulo rotado	$$A = b h$$	$$\bar{x} = \frac{b \cos(\theta) + h \sin(\theta)}{2}$$ $$\bar{y} = \frac{b \sin(\theta) + h \cos(\theta)}{2}$$	$$\bar{I}_x = \frac{b h}{12} (b^2 \sin^2(\theta) + h^2 \cos^2(\theta))$$	$$\bar{I}_y = \frac{b h}{12} (b^2 \cos^2(\theta) + h^2 \sin^2(\theta))$$	Calcular →
Triángulo	$$A = \frac{b h}{2}$$	$$\bar{x} = \frac{a + b}{3}$$ $$\bar{y} = \frac{h}{3}$$	$$\bar{I}_x = \frac{b h^3}{36}$$	$$\bar{I}_y = \frac{bh(a^2-ab+b^2)}{36}$$	Calcular →
Trapecio isósceles	$$A = \frac{h(a + b)}{2}$$	$$\bar{x} = \frac{b}{2}$$ $$\bar{y} = \frac{h(2a + b)}{3(a + b)}$$	$$\bar{I}_x = \frac{h^3(a^2 + 4ab + b^2)}{36(a + b)}$$	$$\bar{I}_y = \frac{h(a + b)(a^2 + b^2)}{48}$$	Calcular →
Trapecio general	$$A = \frac{h(a + b)}{2}$$	$$\bar{x} = \frac{a^2 + ab + 2ac + b^2 + bc}{3(a + b)}$$ $$\bar{y} = \frac{h(2a + b)}{3(a + b)}$$	$$\bar{I}_x = \frac{h^3(a^2 + 4ab + b^2)}{36(a + b)}$$	$$\bar{I}_y = I_y - \bar{x}^2 A$$	Calcular →

Figuras circulares

Sección	Área	Centroide	Inercia respecto a x̄	Inercia respecto a ȳ
Círculo	$$A = \pi r^2$$	$$\bar{x} = r$$ $$\bar{y} = r$$	$$\bar{I}_x = \frac{\pi r^4}{4}$$	$$\bar{I}_y = \frac{\pi r^4}{4}$$	Calcular →
Semicírculo	$$A = \frac{\pi r^2}{2}$$	$$\bar{x} = 0$$ $$\bar{y} = \frac{4r}{3\pi}$$	$$\bar{I}_x = \left(\frac{\pi}{8} - \frac{8}{9\pi}\right) r^4$$	$$\bar{I}_y = \frac{\pi r^4}{8}$$	Calcular →
Cuarto de círculo	$$A = \frac{\pi r^2}{4}$$	$$\bar{x} = \frac{4r}{3\pi}$$ $$\bar{y} = \frac{4r}{3\pi}$$	$$\bar{I}_x = \left(\frac{\pi}{16} - \frac{4}{9\pi}\right) r^4$$	$$\bar{I}_y = \left(\frac{\pi}{16} - \frac{4}{9\pi}\right) r^4$$	Calcular →
Sector circular	$$A = \frac{\theta r^2}{2}$$	$$\bar{x} = \frac{4r \sin(\theta/2)}{3\theta}$$ $$\bar{y} = 0$$	$$\bar{I}_x = \frac{r^4(\theta - \sin\theta)}{8}$$	$$\bar{I}_y = I_y - \bar{x}^2 A$$	Calcular →

Secciones huecas y de pared delgada

Sección	Área	Centroide	Inercia respecto a x̄	Inercia respecto a ȳ
Rectángulo hueco	$$A = b h - b_i h_i$$	$$\bar{x} = \frac{b}{2}$$ $$\bar{y} = \frac{h}{2}$$	$$\bar{I}_x = \frac{b h^3}{12} - \frac{b_i h_i^3}{12}$$	$$\bar{I}_y = \frac{b^3 h}{12} - \frac{b_i^3 h_i}{12}$$	Calcular →
Rectángulo de pared delgada	$$A = b h - b_i h_i$$	$$\bar{x} = \frac{b}{2}$$ $$\bar{y} = \frac{h}{2}$$	$$\bar{I}_x = \frac{b h^3}{12} - \frac{b_i h_i^3}{12}$$	$$\bar{I}_y = \frac{b^3 h}{12} - \frac{b_i^3 h_i}{12}$$	Calcular →
Círculo hueco	$$A = \pi (R^2 - r^2)$$	$$\bar{x} = R$$ $$\bar{y} = R$$	$$\bar{I}_x = \frac{\pi}{4} (R^4 - r^4)$$	$$\bar{I}_y = \frac{\pi}{4} (R^4 - r^4)$$	Calcular →
Círculo de pared delgada	$$A = \pi (R^2 - r^2)$$	$$\bar{x} = R$$ $$\bar{y} = R$$	$$\bar{I}_x = \frac{\pi}{4} (R^4 - r^4)$$	$$\bar{I}_y = \frac{\pi}{4} (R^4 - r^4)$$	Calcular →

Polígonos regulares

Sección	Área	Centroide	Inercia respecto a x̄	Inercia respecto a ȳ
Hexágono	$$A = \frac{3\sqrt{3}}{2}l^2$$	$$\bar{x} = l$$ $$\bar{y} = \frac{\sqrt{3}}{2}l$$	$$\bar{I}_x = \frac{5\sqrt{3}}{16}l^4$$	$$\bar{I}_y = \frac{5\sqrt{3}}{16}l^4$$	Calcular →
Octágono	$$A = 2(\sqrt{2}+1) l^2$$	$$\bar{x} = \frac{\sqrt{2}+1}{2} l$$ $$\bar{y} = \frac{\sqrt{2}+1}{2} l$$	$$\bar{I}_x = \frac{11+8\sqrt{2}}{12} l^4$$	$$\bar{I}_y = \frac{11+8\sqrt{2}}{12} l^4$$	Calcular →

Perfiles estructurales

Sección	Área	Centroide	Inercia respecto a x̄	Inercia respecto a ȳ
Viga I	$$A = td +2s(b -t)$$	$$\bar{x} = \frac{b}{2}$$ $$\bar{y} = \frac{d}{2}$$	$$\bar{I}_x = \frac{bs^3}{6} +\frac{bs(d-s)^2}{2} +\frac{t(d-2s)^3}{12}$$	$$\bar{I}_y = \frac{b^3s}{6} +\frac{t^3(d -2s)}{12}$$	Calcular →
Viga I de alas inclinadas	$$A = dt + (b-t)(g+s)$$	$$\bar{x} = \frac{b}{2}$$ $$\bar{y} = \frac{d}{2}$$	$$\bar{I}_x = \frac{d^3 t}{12} + \frac{(b - t)(3d^2(g + s) - 4d(g^2 + gs + s^2) + 2(g + s)(g^2 + s^2))}{12}$$	$$\bar{I}_y = \frac{d t^3}{12} + \frac{(b-t)((b + t)^2(g + s) + 2(gt^2 + sb^2))}{24}$$	Calcular →
Viga I de alas desiguales	$$A = dt+s_1(b_1-t)+s_2(b_2-t)$$	$$\bar{x} = \frac{\text{max}(b_1,b_2)}{2}$$ —	—	$$\bar{I}_y = \frac{dt^3 + s_1(b_1^3-t^3) + s_2(b_2^3 - t^3)}{12}$$	Calcular →
Viga T	$$A = bs+t(d-s)$$	$$\bar{x} = \frac{b}{2}$$ $$\bar{y} = \frac{bs(2d-s)+t(d-s)^2}{2A}$$	$$\bar{I}_x = I_x - \bar{y}^2 A$$	$$\bar{I}_y = \frac{b^3s}{12} + \frac{t^3(d-s)}{12}$$	Calcular →
Viga T de alma variable	$$A = bs + \frac{(d-s)(t_1+t_2)}{2}$$	$$\bar{x} = \frac{b}{2}$$ $$\bar{y} = \frac{3bs(2d-s) + (d-s)^2(t_1+2t_2)}{6A}$$	$$\bar{I}_x = I_x - \bar{y}^2 A$$	$$\bar{I}_y = \frac{b^3s}{12} + \frac{(d-s)(t_1+t_2)(t_1^2+t_2^2)}{48}$$	Calcular →
Perfil canal C	$$A = 2bs + t(d-2s)$$	$$\bar{x} = \frac{2b^2s + t^2(d-2s)}{4bs + 2t(d-2s)}$$ $$\bar{y} = \frac{d}{2}$$	$$\bar{I}_x = I_x - \bar{y}^2A$$	$$\bar{I}_y = I_y - \bar{x}^2A$$	Calcular →
Canal de alas inclinadas	$$A = bd - (b-t)(d-n-s)$$	$$\bar{x} = \frac{2b^2(n+2s) + 2b(n-s)t + (3d-4n-2s)t^2}{6A}$$ $$\bar{y} = \frac{d}{2}$$	$$\bar{I}_x = I_x - \bar{y}^2A$$	—	Calcular →
Ángulo de lados iguales	$$A = a^2 - (a-t)^2$$	$$\bar{x} = \frac{a^2 + at - t^2}{2(2a - t)}$$ $$\bar{y} = \frac{a^2 + at - t^2}{2(2a - t)}$$	$$\bar{I}_x = I_x - \bar{y}^2 A$$	$$\bar{I}_y = I_y - \bar{x}^2 A$$	Calcular →
Ángulo de lados desiguales	$$A = t(a + b - t)$$	$$\bar{x} = \frac{at+b^2-t^2}{2(a+b-t)}$$ $$\bar{y} = \frac{a^2+bt-t^2}{2(a+b-t)}$$	$$\bar{I}_x = I_x - \bar{y}^2 A$$	$$\bar{I}_y = I_y - \bar{x}^2 A$$	Calcular →
Perfil Z	$$A = t(2b + d - 2t)$$	$$\bar{x} = b-\frac{t}{2}$$ $$\bar{y} = \frac{d}{2}$$	$$\bar{I}_x = \frac{t(2b(3d^2-6dt+4t^2) + (d-2t)^3)}{12}$$	$$\bar{I}_y = \frac{t((2b-t)^3+t^2(d-t))}{12}$$	Calcular →

Notación y ejes

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